Question

If the resistance of a conductor is 5 $\Omega$ at 50${}^o$ C & 7$\Omega$ at 100${}^o$C, then mean temperature coefficient of resistance (of material) is

• A. 0.013/${}^o$C
• B. 0.004/${}^o$C
• C. 0.006/${}^o$C
• D. 0.008/${}^o$C

Answer 1

The correct option is A 0.013/${}^o$C

We know that $R_T=R_0(1+\alpha T)$ where $R_T=$ resistance at temp T, $R_0=$ resistance at temp $T=0^{o}C$ and $\alpha =$ temperature coefficient of resistance.

Here, $5=R_0(1+\alpha .50)...\left(1\right)$
and $7=R_0(1+\alpha .100)...\left(2\right)$
$\left(2\right)/\left(1\right)\Rightarrow \frac{7}{5}=\frac{1+100\alpha }{1+50\alpha }$
$7+350\alpha =5+500\alpha$
$150\alpha =2\Rightarrow \alpha =2/150=0.013{/}^{o}C$